Conway groups

E29418

family of sporadic simple groups finite group finite simple group lattice in 24-dimensional Euclidean space mathematical concept mathematician sporadic simple group

Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.

Aliases (7)

Conway group Co1 ×8
automorphism group of the Leech lattice ×8
Conway group Co2 ×7
Conway group Co3 ×7
John Horton Conway ×3
Leech lattice ×3
Conway group ×2

Statements (48)

Predicate	Object
instanceOf	family of sporadic simple groups → finite group → finite simple group → finite simple group → finite simple group → lattice in 24-dimensional Euclidean space → mathematical concept → mathematician → sporadic simple group → sporadic simple group → sporadic simple group →
classification	part of the 26 sporadic simple groups →
consistOf	Co1 → Co2 → Co3 →
containsSubgroup	Conway group Co1 → Conway group Co2 → Conway group Co3 →
definedOver	finite sets →
dimension	24 →
discoveredBy	John Horton Conway →
discoveryContext	study of symmetries of the Leech lattice →
field	group theory → group theory →
hasAutomorphismGroup	automorphism group of the Leech lattice →
hasCardinality	3 →
hasMember	Conway group Co1 → Conway group Co2 → Conway group Co3 →
hasProperty	centerless → finite simple groups → non-abelian → non-abelian → non-abelian → non-abelian simple groups →
isSubgroupOf	automorphism group of the Leech lattice → automorphism group of the Leech lattice → automorphism group of the Leech lattice →
isSubsetOf	sporadic simple groups →
knownFor	discovery of Conway groups →
namedAfter	John Horton Conway →
order	4157776806543360000 → 42305421312000 → 495766656000 →
relatedTo	Leech lattice → Monster group → automorphism group of the Leech lattice →
yearDiscoveredApprox	1960s →

Referenced by (15)

Subject (surface form when different)	Predicate
automorphism group of the Leech lattice ("Conway group Co1") → automorphism group of the Leech lattice ("Conway group Co2") → automorphism group of the Leech lattice ("Conway group Co3") →	containsSubgroup
Conway groups ("Conway group Co1") → Conway groups ("Conway group Co2") → Conway groups ("Conway group Co3") →	hasMember
John H. Conway → John H. Conway → John Horton Conway ("Conway group") →	notableWork
Conway group Co1 ("automorphism group of the Leech lattice") → Conway group Co2 ("automorphism group of the Leech lattice") →	isSubgroupOf
Conway groups ("automorphism group of the Leech lattice") → Monster group construction (with collaborators) →	relatedTo
Leech lattice ("automorphism group of the Leech lattice") →	hasAutomorphismGroup
John H. Conway ("Conway group") →	hasConcept